Geometry

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Elements[edit | edit source]

  • Among the numerous reflections of Jesus Christ there is a fairly unexpected one. Christ is described in some of the 'ancient' sources as the 'ancient' Greek mathematician Euclid, to whom 'Elements', a famous book on geometry, is attributed. Presumably, the Emperor Andronicus-Christ was a patron of science, was interested in mathematics and by his order and maybe even under his supervision, the definitive work 'Elements' was created. By the way, the name Euclid is just a slight variation on the word KOLIADA one of Christ's names.
    • Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians. However, Euclid is generally credited with arranging these theorems in a logical manner, so as to demonstrate (admittedly, not always with the rigour demanded by modern mathematics) that they necessarily follow from five simple axioms. Euclid is also credited with devising a number of particularly ingenious proofs of previously discovered theorems: e.g. Theorem 48 in Book 1.
  • The geometrical constructions employed in the Elements are restricted to those which can be achieved using a straight-rule and a compass. Furthermore, empirical proofs by means of measurement are strictly forbidden: i.e., any comparison of two magnitudes is restricted to saying that the magnitudes are either equal, or that one is greater than the other. The Elements consists of thirteen books.
    • Book 1 outlines the fundamental propositions of plane geometry, including the three cases in which triangles are congruent, various theorems involving parallel lines, the theorem regarding the sum of the angles in a triangle, and the Pythagorean theorem.
    • Book 2 is commonly said to deal with “geometric algebra”, since most of the theorems contained within it have simple algebraic interpretations.
    • Book 3 investigates circles and their properties, and includes theorems on tangents and inscribed angles.
    • Book 4 is concerned with regular polygons inscribed in, and circumscribed around, circles.
    • Book 5 develops the arithmetic theory of proportion.
    • Book 6 applies the theory of proportion to plane geometry, and contains theorems on similar figures.
    • Book 7 deals with elementary number theory: e.g., prime numbers, greatest common denominators, etc.
    • Book 8 is concerned with geometric series.
    • Book 9 contains various applications of results in the previous two books, and includes theorems on the infinitude of prime numbers, as well as the sum of a geometric series.
    • Book 10 attempts to classify incommensurable (i.e., irrational) magnitudes using the so-called “method of exhaustion”, an ancient precursor to integration.
    • Book 11 deals with the fundamental propositions of three-dimensional geometry.
    • Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion.
    • Book 13 investigates the five so-called Platonic solids.

History[edit | edit source]

1st century AC[edit | edit source]